Seasonal Amplification of the 2-Day Wave: Relationship between Normal Mode and Instability

Abstract

The 2-day wave is a prominent feature of the middle and upper atmosphere, amplifying twice-yearly around solstice. Its period, structure, and reproducibility have led to its association with the gravest planetary normal mode of zonal wavenumber 3, the so-called Rossby-gravity mode. On the other hand, its amplification around solstice has also led to its association with baroclinic instability of summer easterlies. To explore the relationship between the Rossby-gravity mode and instability, calculations are performed with the linearized primitive equations that have been generalized to account for that mode's interaction with a generally unstable mean flow u. The mode's eigenfrequency is then complex, the imaginary component representing amplification and decay. For mean states representative of solstice and equinox, the normal mode is calculated and then compared to observed behavior in terms of its period, structure, and amplification. The behavior recovered, including structural differences between solstice and equinox, is consistent with major features of the 2-day wave. Under solstitial conditions, the Rossby-gravity mode amplifies by extracting energy from the mean flow, with e-folding times as short as 5 days. Even though its eigenfrequency is then complex, the mode's period remains close to the theoretical value, consistently lying at westward periods of 2.0?2.2 days. Equally robust is its eigenstructure, which extends into both hemispheres. It mirrors the modal structure isolated earlier in the response over real frequency. In contrast, the mode's amplification depends sensitively upon details of the zonal-mean state. Changes of u that are modest, in some instances subtle, are sufficient to remove instability. Those changes of mean flow sharply alter the mode's growth rate, but have little effect on its eigenperiod and structure.